Questions: Consider a 4d orbital. a. What are the allowed values for the n and l quantum numbers for a 4d orbital? n= b. What are the allowed values for the ml quantum number for a 4d orbital? 0 -1,0,1 -2,-1,0,1,2 -3,-2,-1,0,1,2,3 c. What is the maximum number of 4d orbitals that could be present in any one atom? 4d orbitals d. What is the maximum number of electrons that could occupy a single 4d orbital? electron(s)

Consider a 4d orbital.
a. What are the allowed values for the n and l quantum numbers for a 4d orbital?
n=
b. What are the allowed values for the ml quantum number for a 4d orbital?
0
-1,0,1
-2,-1,0,1,2
-3,-2,-1,0,1,2,3
c. What is the maximum number of 4d orbitals that could be present in any one atom?
4d orbitals
d. What is the maximum number of electrons that could occupy a single 4d orbital?
electron(s)

Transcript text: Consider a $4 d$ orbital. a. What are the allowed values for the $n$ and $\ell$ quantum numbers for a $4 d$ orbital? $n=$ $\square$ $\square$ b. What are the allowed values for the $m_{\ell}$ quantum number for a $4 d$ orbital? 0 $-1,0,1$ $-2,-1,0,1,2$ $-3,-2,-1,0,1,2,3$ c. What is the maximum number of $4 d$ orbitals that could be present in any one atom? $\square$ $4 d$ orbitals d. What is the maximum number of electrons that could occupy a single $4 d$ orbital? $\square$ electron(s)

Solution

Solution Steps

Step 1: Determine the Allowed Values for $ n $ and $ \ell $ Quantum Numbers

For a $ 4d $ orbital:

The principal quantum number $ n $ is 4.
The azimuthal quantum number $ \ell $ for a $ d $ orbital is 2.

Thus, the allowed values are: \[ n = 4 \] \[ \ell = 2 \]

Step 2: Determine the Allowed Values for $ m_{\ell} $ Quantum Number

The magnetic quantum number $ m_{\ell} $ can take values from $-\ell$ to $+\ell$, including zero. For $ \ell = 2 $: \[ m_{\ell} = -2, -1, 0, 1, 2 \]

Step 3: Determine the Maximum Number of $ 4d $ Orbitals

The number of orbitals for a given $ \ell $ value is $ 2\ell + 1 $. For $ \ell = 2 $: \[ 2(2) + 1 = 5 \] So, there are 5 possible $ 4d $ orbitals.

Step 4: Determine the Maximum Number of Electrons in a Single $ 4d $ Orbital

Each orbital can hold a maximum of 2 electrons (one with spin up and one with spin down).

Final Answer

a. The allowed values for the $ n $ and $ \ell $ quantum numbers for a $ 4d $ orbital are: \[ \boxed{n = 4} \] \[ \boxed{\ell = 2} \]

b. The allowed values for the $ m_{\ell} $ quantum number for a $ 4d $ orbital are: \[ \boxed{-2, -1, 0, 1, 2} \]

c. The maximum number of $ 4d $ orbitals that could be present in any one atom is: \[ \boxed{5 \text{ } 4d \text{ orbitals}} \]

d. The maximum number of electrons that could occupy a single $ 4d $ orbital is: \[ \boxed{2 \text{ electron(s)}} \]

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